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Improved Sufficient Conditions for Hamiltonian Properties

References [1] J.-P. Bode, A. Kemnitz, I. Schiermeyer and A. Schwarz, Generalizing Bondy’s theorems on sufficient conditions for Hamiltonian properties, Congr. Numer. 203 (2010) 5-13. [2] J.A. Bondy, Longest paths and cycles in graphs of high degree, Research Report CORR 80-16 (Department of Combinatorics and Optimization, Faculty of Mathe- matics, University of Waterloo, Waterloo, Ontario, Canada, 1980). [3] J.A. Bondy and V. Chvátal, A method in graph theory, Discrete Math. 15 (1976) 111-135. doi:10

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On Vertices Enforcing a Hamiltonian Cycle

References [1] C.A. Barefoot, Hamiltonian connectivity of the Halin graphs, Congr. Numer. 58 (1987) 93-102. [2] J.A. Bondy, Pancyclic graphs: recent results, in: Infinite and finite sets, Vol. 1, Colloq. Math. Soc. J´anos Bolyai 10, A. Hajnal, R. Rado and V.T. S´os (Ed(s)), (North Holland, 1975) 181-187. [3] J.A. Bondy and L. Lovász, Cycles through specified vertices of a graph, Combinatorica 1 (1981) 117-140. doi:10.1007/BF02579268 [4] H.J. Broersma and H.J. Veldman, 3-connected line

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On the Hamiltonian Number of a Plane Graph

References [1] M. Araya and G. Wiener, On cubic planar hypohamiltonian and hypotraceable graphs, Electron. J. Combin. 18 (2011) #P85. [2] T. Asano, T. Nishizeki and T. Watanabe, An upper bound on the length of a Hamil- tonian walk of a maximal planar graph, J. Graph Theory 4 (1980) 315-336. doi: 10.1002/jgt.3190040310 [3] J.-C. Bermond, On Hamiltonian walks, in: Proceedings of the Fifth British Combinatorial Conference, Util. Math., Winnipeg, Man. (1975) 41-51. [4] J.A. Bondy and U.S.R. Murty

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Hamiltonian Normal Cayley Graphs

R eferences [1] N. Alon and Y. Roichman, Random Cayley graphs and expanders , Random Structures Algorithms 5 (1994) 271–284. doi:10.1002/rsa.3240050203 [2] J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, New York, 2008). [3] J. Bourgain and A. Gamburd, Uniform expansion bounds for Cayley graphs of SL 2 (ℱ p ), Ann. of Math. 167 (2008) 625–642. doi:10.4007/annals.2008.167.625 [4] C.C. Chen and N. Quimpo, On strongly hamiltonian abelian group graphs , Combin. Math. VIII (Geelong, 1980) Lecture Notes in Math. 884 (Springer

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On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs

References [1] S. Abbasi and A. Jamshed, A degree constraint for uniquely Hamiltonian graphs, Graphs Combin. 22 (2006) 433-442. doi:10.1007/s00373-006-0666-z [2] H. Bielak, Chromatic properties of Hamiltonian graphs, Discrete Math. 307 (2007) 1245-1254. doi:10.1016/j.disc.2005.11.061 [3] J.A. Bondy and B. Jackson, Vertices of small degree in uniquely Hamiltonian graphs, J. Combin. Theory (B) 74 (1998) 265-275. doi:10.1006/jctb.1998.1845 [4] R.C. Entringer and H. Swart, Spanning cycles of nearly

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On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes

References [1] J.A. Bondy and and U.S.R. Murty, Graph Theory with Applications (Macmillan Press, London, 1976). doi: 10.1007/978-1-349-03521-2 [2] R.X. Hao, R. Zhang, Y.Q. Feng and J.X. Zhou, Hamiltonian cycle embedding for fault tolerance in balanced hypercubes, Appl. Math. Comput. 244 (2014) 447-456. doi: 10.1016/j.amc.2014.07.015 [3] S.Y. Hsieh, G.H. Chen and C.W. Ho, Hamiltonian-laceability of star graphs, Net- works 36 (2000) 225-232. doi: 10.1002/1097-0037(200012)36:4h225::AID-NET3i3.0.CO;2-G

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Matchings Extend to Hamiltonian Cycles in 5-Cube

R eferences [1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (North-Holland, New York-Amsterdam-Oxford, 1982). [2] R. Caha and V. Koubek, Spanning multi-paths in hypercubes , Discrete Math. 307 (2007) 2053–2066. doi:10.1016/j.disc.2005.12.050 [3] D. Dimitrov, T. Dvořák, P. Gregor and R. Škrekovski, Gray codes avoiding matchings , Discrete Math. Theoret. Comput. Sci. 11 (2009) 123–148. [4] T. Dvořák, Hamiltonian cycles with prescribed edges in hypercubes , SIAM J. Discrete Math. 19 (2005) 135–144. doi:10.1137/S

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Arc-Disjoint Hamiltonian Cycles in Round Decomposable Locally Semicomplete Digraphs

. Huang, Decomposing locally semicomplete digraphs into strong spanning subdigraphs , J. Combin. Theory Ser. B 102 (2012) 701–714. doi:10.1016/j.jctb.2011.09.001 [5] Y. Guo, Locally Semicomplete Digraphs (Ph.D. Thesis, RWTH Aachen University, 1995). [6] Y. Guo, Strongly Hamiltonian-connected locally semicomplet digraphs , J. Graph Theory 21 (1996) 65–73. doi:10.1002/(SICI)1097-0118(199605)22:1h65::AID-JGT9i3.0.CO;2-J [7] F. Harary and L. Moser, The theory of round robin tournaments , Amer. Math. Monthly 73 (1966) 231–246. doi:10

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A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model

velocities measurement, Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, CA, USA, pp. 1521-1526. Rodríguez Alfaro, L.H. (2014). Active Fault Tolerant Control of Hamiltonian Convergent Systems, Ph.D. thesis, Autonomous University of Nuevo Leon, San Nicolas de los Garza, (in Spanish). Seliger, R. and Frank, P.M. (1991). Fault diagnosis by disturbance decoupled nonlinear observers, CDC ’91, Brighton, UK, pp. 2248-2253. Sira Ramírez, H. and Cruz Hernández, C. (2001). Synchronization of chaotic systems: A

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On the H-Force Number of Hamiltonian Graphs and Cycle Extendability

R eferences [1] A. Abueida and R. Sritharan, Cycle extendability and Hamiltonian cycles in chordal graph classes , SIAM J. Discrete Math. 20 (2006) 669–681. doi:10.1137/S0895480104441267 [2] G. Chen, R.J. Faudree, R.J. Gould and M.S. Jacobson, Cycle extendability of Hamiltonian interval graphs , SIAM J. Discrete Math. 20 (2006) 682–689. doi:10.1137/S0895480104441450 [3] R. Diestel, Graph Theory (Springer, Graduate Texts in Mathematics 173 , 2005). [4] I. Fabrici, E. Hexel and S. Jendrol’, On vertices enforcing a Hamiltonian cycle

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